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Mathematics Colloquium

Alexandra Smirnova
Georgia State University

Title: On iteratively regularized alternating minimization algorithm for stable parameter estimation in epidemiology
Date: Friday, March 24, 2023
Place and Time: LOV 101, 3:05-3:55 pm


A nonlinear constrained optimization problem motivated by various challenges of stable parameter estimation in epidemiology is presented. A hybrid iteratively regularized alternating minimization (IRAM) scheme is introduced that builds upon all-at-once formulation, recently developed by Kaltenbacher and her co-authors for nonlinear constrained least squares (2016), the generalized profiling methods by Ramsay, Hooker, Campbell, and Cao (2007) for estimating parameters in nonlinear ordinary differential equations, and the so-called traditional route for solving nonlinear ill-posed problems, pioneered by Bakushinsky (1991). Similar to the all-at-once approach, our proposed algorithm does not require an explicit deterministic or stochastic trajectory of system evolution. At the same time, the predictor-corrector framework of the new method avoids the difficulty of dealing with large solution spaces resulting from all-at-once make-up, which inevitably leads to oversized Jacobian and Hessian approximations. Therefore, our IRAM algorithm has the potential to save time and storage, which is critical when multiple runs of the iterative scheme are carried out for uncertainty quantification. The new procedure takes full advantage of the iterative regularization framework, and it is not limited to the constraints in the form of differential equations (or systems of differential equations). Theoretical findings are illustrated with numerical experiments carried out using real data on COVID-19 pandemic.